Mathematicians Bridge the Divide Between Infinity and the Physical World

Even though they questioned the value and consistency of infinitistic logic, Hilbert and his contemporaries did not wish to give up such abstractions--power tools of mathematical reasoning that in 1928 would enable the British philosopher and mathematician Frank Ramsey to chop up and color infinite sets at will. "No one shall expel us from the paradise which Cantor has created for us," Hilbert said in a 1925 lecture. He hoped to stay in Cantor's paradise and obtain proof that it stood on stable logical ground. Hilbert tasked mathematicians with proving that set theory and all of infinitistic mathematics is finitistically reducible, and therefore trustworthy. "We must know; we will know!" he said in a 1930 address in Königsberg--words later etched on his tomb.